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Metrics on Hitchin Components from Hölder Distortion

2024/02/26 by Alexander Nolte, Nolte, Alexander
Engineering · #Metal Forming Simulation Techniques #Advanced Numerical Analysis Techniques

paper · pdf · doi:10.48550/arxiv.2402.16584

Abstract

We observe Thurston's asymmetric metric on Teichmüller space may be expressed in terms of the Hölder regularity of boundary maps. We then associate 2-dimensional stratified loci in \mathbbRPn-1 to PSLn(ℝ) Hitchin representations with n > 3. We prove that measuring the relative Hölder distortion of these loci gives asymmetric metrics on the Hitchin component Hitn(S) with complete and geometrically meaningful symmetrizations. These are the first known geometrically significant complete metrics on Hitn(S) for n > 3.

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